POSITION SENSING METHOD AND POSITION SENSOR, EXPOSING METHOD AND EXPOSING APPARATUS, AND DEVICE AND DEVICE MANUFACTURING METHOD

摘要

On the basis of information on the position of a mark contained in a set of a plurality of measured samples, a parameter calculation unit (33) statistically determines the estimations and their certainties of a predetermined number of parameters for uniquely specifying a given position on a body for each sample set. On the basis of the estimations and the certainties of the predetermined number of parameters for each sample set, a validity calculating unit (34) determines the values of a predetermined statistically valid number of parameters. An evaluating unit (35) statistically judges whether or not the number of marks contained in the sample set can be reduced. After the reduction is judged to be possible, the parameter calculation unit (33) determines the values of the predetermined number of parameters by using another sample set where the number of marks is reduced. By using the values of the number of parameters thus determined, the position of any region on the object can be highly accurately determined.